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2sin^2x+3sinx-2>0 and x^2-x-2<0. Find th...

`2sin^2x+3sinx-2>0 and x^2-x-2<0.` Find the solution set.

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Evaluate the following limits: lim_(x to(pi)/(6))(2sin^(2)x+sinx-1)/(2sin^(2)x-3sinx+1)

Evaluate the following limits: lim_(xrarr pi//6)((2sin^(2)x+sinx-1))/((2sin^(2)x-3sinx+1))

Knowledge Check

  • lim_(x to pi//6) (2sin^2x+sinx-1)/(2sin^2x-3sinx+1)=

    A
    3
    B
    -3
    C
    6
    D
    0

  • What is lim_(xto(pi)/(6))(2sin^(2)x+sinx-1)/(2sin^(2)x-3sinx+1) to ?

    A
    A. `-(1)/(2)`
    B
    B. `-(1)/(3)`
    C
    C. `-2`
    D
    D. `-3`

  • If f(x) = (sin^2x + 4sinx + 5)/(2 sin ^2x + 8 sin x + 8) , then range of f(x) is

    A
    `(1/2,oo)`
    B
    `(5/9,1)`
    C
    `[ 5/9, 1]`
    D
    `[5/9,oo)`

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